%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV394^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:41:10 AM UTC 2026
% Result : Theorem 1.00s 0.90s
% Output : Refutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 207 ( 82 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 245 ( 46 ~; 20 |; 47 &; 112 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 28 ^; 41 !; 18 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_8,type,
sK0: a > $o ).
thf(func_def_9,type,
sK1: a > $o ).
thf(func_def_10,type,
sK2: a > $o ).
thf(func_def_11,type,
sK3: a ).
thf(func_def_13,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f29,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f28,f16]) ).
thf(f16,plain,
( ( sK2 @ sK3 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( ^ [Y0: a] :
( ~ ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ( ( sK2 @ sK3 )
!= $true )
& ( $true
= ( sK0 @ sK3 ) )
& ! [X4: a] :
( ( ( sK0 @ X4 )
!= $true )
| ( ( sK1 @ X4 )
= $true )
| ( $true
= ( sK2 @ X4 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f12,f11]) ).
thf(f11,plain,
( ? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] :
( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ? [X3: a] :
( ( ( X2 @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X0 @ X4 )
!= $true )
| ( ( X1 @ X4 )
= $true )
| ( ( X2 @ X4 )
= $true ) ) )
=> ( ( ( ^ [Y0: a] :
( ~ ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ? [X3: a] :
( ( ( sK2 @ X3 )
!= $true )
& ( ( sK0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( sK0 @ X4 )
!= $true )
| ( ( sK1 @ X4 )
= $true )
| ( $true
= ( sK2 @ X4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X3: a] :
( ( ( sK2 @ X3 )
!= $true )
& ( ( sK0 @ X3 )
= $true ) )
=> ( ( ( sK2 @ sK3 )
!= $true )
& ( $true
= ( sK0 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] :
( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ? [X3: a] :
( ( ( X2 @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X0 @ X4 )
!= $true )
| ( ( X1 @ X4 )
= $true )
| ( ( X2 @ X4 )
= $true ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] :
( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ? [X4: a] :
( ( ( X2 @ X4 )
!= $true )
& ( ( X0 @ X4 )
= $true ) )
& ! [X3: a] :
( ( ( X0 @ X3 )
!= $true )
| ( ( X1 @ X3 )
= $true )
| ( ( X2 @ X3 )
= $true ) ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X4: a] :
( ( ( X2 @ X4 )
!= $true )
& ( ( X0 @ X4 )
= $true ) )
& ( ( ^ [Y0: a] :
( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X1 @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ( ^ [Y0: a] :
( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
& ! [X3: a] :
( ( ( ( X1 @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) )
=> ( ( X2 @ X3 )
= $true ) ) )
=> ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
=> ( ( X2 @ X4 )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( ( X0 @ X3 )
= $true )
& ( ( X1 @ X3 )
!= $true ) )
=> ( ( X2 @ X3 )
= $true ) )
& ( ( ^ [Y0: a] :
( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) )
=> ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
=> ( ( X2 @ X4 )
= $true ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( ( X0 @ X3 )
= $true )
& ( ( X1 @ X3 )
!= $true ) )
=> ( ( X2 @ X3 )
= $true ) )
& ( ( ^ [Y0: a] :
( ~ ( X2 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) )
=> ! [X6: a] :
( ( ( X0 @ X6 )
= $true )
=> ( ( X2 @ X6 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( X0 @ X3 )
& ~ ( X1 @ X3 ) )
=> ( X2 @ X3 ) )
& ( ( ^ [X4: a] : $false )
= ( ^ [X5: a] :
( ( X1 @ X5 )
& ~ ( X2 @ X5 ) ) ) ) )
=> ! [X6: a] :
( ( X0 @ X6 )
=> ( X2 @ X6 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ! [X3: a] :
( ( ( X0 @ X3 )
& ~ ( X2 @ X3 ) )
=> ( X1 @ X3 ) )
& ( ( ^ [X3: a] : $false )
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ~ ( X1 @ X3 ) ) ) ) )
=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > $o,X2: a > $o,X1: a > $o] :
( ( ! [X3: a] :
( ( ( X0 @ X3 )
& ~ ( X2 @ X3 ) )
=> ( X1 @ X3 ) )
& ( ( ^ [X3: a] : $false )
= ( ^ [X3: a] :
( ( X2 @ X3 )
& ~ ( X1 @ X3 ) ) ) ) )
=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6MKDivwwtP/DTF2THF_1594.p',cTHM269_pme) ).
thf(f28,plain,
( ( sK2 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f25]) ).
thf(f25,plain,
( ( $false = $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(superposition,[status(thm)],[f24,f20]) ).
thf(f20,plain,
( $true
= ( sK1 @ sK3 ) ),
inference(subsumption_resolution,[status(thm)],[f19,f15]) ).
thf(f15,plain,
( $true
= ( sK0 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f19,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
!= ( sK0 @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true != $true )
| ( $true
!= ( sK0 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f16,f14]) ).
thf(f14,plain,
! [X4: a] :
( ( $true
= ( sK2 @ X4 ) )
| ( ( sK1 @ X4 )
= $true )
| ( ( sK0 @ X4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f24,plain,
! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( ( sK2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: a] :
( ( ( ~ ( sK2 @ X1 ) )
= $false )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: a] :
( ( ~ ( sK2 @ X1 )
& ( sK1 @ X1 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: a] :
( ( ^ [Y0: a] : $false
@ X1 )
= ( ^ [Y0: a] :
( ~ ( sK2 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( ~ ( sK2 @ Y0 )
& ( sK1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEV394^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.06/0.25 % Computer : n012.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue Feb 24 12:46:00 EST 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.06/0.31 ---- Original DTF file ---
% 0.06/0.31 thf(spec,logic,$$dhol).
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 % File : SEV394^5 : TPTP v9.2.1. Released v4.0.0.
% 0.06/0.31 % Domain : Set Theory
% 0.06/0.31 % Problem : TPS problem THM269
% 0.06/0.31 % Version : Especial.
% 0.06/0.31 % English : Example for CADE-15.
% 0.06/0.31
% 0.06/0.31 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.06/0.31 % Source : [Bro09]
% 0.06/0.31 % Names : tps_0317 [Bro09]
% 0.06/0.31 % : THM108 [TPS]
% 0.06/0.31 % : THM269 [TPS]
% 0.06/0.31
% 0.06/0.31 % Status : Theorem
% 0.06/0.31 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.06/0.31 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.06/0.31 % Number of atoms : 2 ( 1 equ; 0 cnn)
% 0.06/0.31 % Maximal formula atoms : 1 ( 2 avg)
% 0.06/0.31 % Number of connectives : 15 ( 2 ~; 0 |; 3 &; 7 @)
% 0.06/0.31 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.06/0.31 % Maximal formula depth : 11 ( 11 avg)
% 0.06/0.31 % Number of types : 2 ( 1 usr)
% 0.06/0.31 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.06/0.31 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.06/0.31 % Number of variables : 7 ( 2 ^; 5 !; 0 ?; 7 :)
% 0.06/0.31 % SPC : TH0_THM_EQU_NAR
% 0.06/0.31
% 0.06/0.31 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.06/0.31 % project in the Department of Mathematical Sciences at Carnegie
% 0.06/0.31 % Mellon University. Distributed under the Creative Commons copyleft
% 0.06/0.31 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.06/0.31 % : Polymorphic definitions expanded.
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 thf(a_type,type,
% 0.06/0.31 a: $tType ).
% 0.06/0.31
% 0.06/0.31 thf(cTHM269_pme,conjecture,
% 0.06/0.31 ! [Xw: a > $o,Xy: a > $o,Xz: a > $o] :
% 0.06/0.31 ( ( ! [Xx: a] :
% 0.06/0.31 ( ( ( Xw @ Xx )
% 0.06/0.31 & ~ ( Xz @ Xx ) )
% 0.06/0.31 => ( Xy @ Xx ) )
% 0.06/0.31 & ( ( ^ [Xx: a] :
% 0.06/0.31 ( ( Xz @ Xx )
% 0.06/0.31 & ~ ( Xy @ Xx ) ) )
% 0.06/0.31 = ( ^ [Xx: a] : $false ) ) )
% 0.06/0.31 => ! [Xx: a] :
% 0.06/0.31 ( ( Xw @ Xx )
% 0.06/0.31 => ( Xy @ Xx ) ) ) ).
% 0.06/0.31
% 0.06/0.31 %------------------------------------------------------------------------------
% 0.06/0.31 ------------------------
% 0.83/0.88 ---- Embedded in THF ---
% 0.83/0.88 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.83/0.88 %%% Generated on Tue Feb 24 12:46:01 EST 2026
% 0.83/0.88 %%% using '$$dhol' embedding, version 1.3.0.
% 0.83/0.88 %%% Logic specification used:
% 0.83/0.88 %%% thf(spec, logic, $$dhol).
% 0.83/0.88
% 0.83/0.88 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6MKDivwwtP/DTF2DTF1594.p
% See solution above
% 0.83/0.88 ------------------------
% 0.83/0.88 ---- Cleaned THF ---
% 0.83/0.88 thf(a_type,type,
% 0.83/0.88 a: $tType ).
% 0.83/0.88
% 0.83/0.88 thf(cTHM269_pme,conjecture,
% 0.83/0.88 ! [Xw: a > $o,Xy: a > $o,Xz: a > $o] :
% 0.83/0.88 ( ( ! [Xx: a] :
% 0.83/0.88 ( ( ( Xw @ Xx )
% 0.83/0.88 & ~ ( Xz @ Xx ) )
% 0.83/0.88 => ( Xy @ Xx ) )
% 0.83/0.88 & ( ( ^ [Xx: a] :
% 0.83/0.88 ( ( Xz @ Xx )
% 0.83/0.88 & ~ ( Xy @ Xx ) ) )
% 0.83/0.88 = ( ^ [Xx: a] : $false ) ) )
% 0.83/0.88 => ! [Xx: a] :
% 0.83/0.88 ( ( Xw @ Xx )
% 0.83/0.88 => ( Xy @ Xx ) ) ) ).
% 0.83/0.88 ------------------------
% 1.00/0.90 % (1809)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_1594 for (3000ds/4Mi)
% 1.00/0.90 % (1810)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_1594 for (3000ds/27Mi)
% 1.00/0.90 % (1811)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1594 for (3000ds/2Mi)
% 1.00/0.90 % (1812)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_1594 for (3000ds/2Mi)
% 1.00/0.90 % (1808)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1594 for (3000ds/183Mi)
% 1.00/0.90 % (1813)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_1594 for (3000ds/275Mi)
% 1.00/0.90 % (1814)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1594 for (3000ds/18Mi)
% 1.00/0.90 % (1811)Instruction limit reached!
% 1.00/0.90 % (1811)------------------------------
% 1.00/0.90 % (1811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.90 % (1811)Termination reason: Unknown
% 1.00/0.90 % (1811)Termination phase: Saturation
% 1.00/0.90
% 1.00/0.90 % (1811)Memory used [KB]: 5500
% 1.00/0.90 % (1811)Time elapsed: 0.002 s
% 1.00/0.90 % (1811)Instructions burned: 2 (million)
% 1.00/0.90 % (1811)------------------------------
% 1.00/0.90 % (1811)------------------------------
% 1.00/0.90 % (1812)Instruction limit reached!
% 1.00/0.90 % (1812)------------------------------
% 1.00/0.90 % (1812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.90 % (1812)Termination reason: Unknown
% 1.00/0.90 % (1812)Termination phase: Saturation
% 1.00/0.90
% 1.00/0.90 % (1812)Memory used [KB]: 5500
% 1.00/0.90 % (1812)Time elapsed: 0.002 s
% 1.00/0.90 % (1812)Instructions burned: 2 (million)
% 1.00/0.90 % (1812)------------------------------
% 1.00/0.90 % (1812)------------------------------
% 1.00/0.90 % (1808)First to succeed.
% 1.00/0.90 % (1813)Also succeeded, but the first one will report.
% 1.00/0.90 % (1808)Refutation found. Thanks to Tanya!
% 1.00/0.90 % SZS status Theorem for DTF2THF_1594
% 1.00/0.90 % SZS output start Proof for DTF2THF_1594
% 1.00/0.90 thf(type_def_5, type, a: $tType).
% 1.00/0.90 thf(func_def_0, type, a: $tType).
% 1.00/0.90 thf(func_def_8, type, sK0: a > $o).
% 1.00/0.90 thf(func_def_9, type, sK1: a > $o).
% 1.00/0.90 thf(func_def_10, type, sK2: a > $o).
% 1.00/0.90 thf(func_def_11, type, sK3: a).
% 1.00/0.90 thf(func_def_13, type, ph5: !>[X0: $tType]:(X0)).
% 1.00/0.90 thf(f29,plain,(
% 1.00/0.90 $false),
% 1.00/0.90 inference(subsumption_resolution,[status(thm)],[f28,f16])).
% 1.00/0.90 thf(f16,plain,(
% 1.00/0.90 ((sK2 @ sK3) != $true)),
% 1.00/0.90 inference(cnf_transformation,[status(thm)],[f13])).
% 1.00/0.90 thf(f13,plain,(
% 1.00/0.90 ((^[Y0 : a]: ((~ (sK2 @ Y0)) & (sK1 @ Y0))) = (^[Y0 : a]: ($false))) & (((sK2 @ sK3) != $true) & ($true = (sK0 @ sK3))) & ! [X4 : a] : (((sK0 @ X4) != $true) | ((sK1 @ X4) = $true) | ($true = (sK2 @ X4)))),
% 1.00/0.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f10,f12,f11])).
% 1.00/0.90 thf(f11,plain,(
% 1.00/0.90 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (((^[Y0 : a]: ((~ (X2 @ Y0)) & (X1 @ Y0))) = (^[Y0 : a]: ($false))) & ? [X3 : a] : (((X2 @ X3) != $true) & ((X0 @ X3) = $true)) & ! [X4 : a] : (((X0 @ X4) != $true) | ((X1 @ X4) = $true) | ((X2 @ X4) = $true))) => (((^[Y0 : a]: ((~ (sK2 @ Y0)) & (sK1 @ Y0))) = (^[Y0 : a]: ($false))) & ? [X3 : a] : (((sK2 @ X3) != $true) & ((sK0 @ X3) = $true)) & ! [X4 : a] : (((sK0 @ X4) != $true) | ((sK1 @ X4) = $true) | ($true = (sK2 @ X4))))),
% 1.00/0.90 introduced(definition,[],[choice_axiom])).
% 1.00/0.90 thf(f12,plain,(
% 1.00/0.90 ? [X3 : a] : (((sK2 @ X3) != $true) & ((sK0 @ X3) = $true)) => (((sK2 @ sK3) != $true) & ($true = (sK0 @ sK3)))),
% 1.00/0.90 introduced(definition,[],[choice_axiom])).
% 1.00/0.90 thf(f10,plain,(
% 1.00/0.90 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (((^[Y0 : a]: ((~ (X2 @ Y0)) & (X1 @ Y0))) = (^[Y0 : a]: ($false))) & ? [X3 : a] : (((X2 @ X3) != $true) & ((X0 @ X3) = $true)) & ! [X4 : a] : (((X0 @ X4) != $true) | ((X1 @ X4) = $true) | ((X2 @ X4) = $true)))),
% 1.00/0.90 inference(rectify,[status(thm)],[f9])).
% 1.00/0.90 thf(f9,plain,(
% 1.00/0.90 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (((^[Y0 : a]: ((~ (X2 @ Y0)) & (X1 @ Y0))) = (^[Y0 : a]: ($false))) & ? [X4 : a] : (((X2 @ X4) != $true) & ((X0 @ X4) = $true)) & ! [X3 : a] : (((X0 @ X3) != $true) | ((X1 @ X3) = $true) | ((X2 @ X3) = $true)))),
% 1.00/0.90 inference(flattening,[status(thm)],[f8])).
% 1.00/0.90 thf(f8,plain,(
% 1.00/0.90 ? [X0 : a > $o,X1 : a > $o,X2 : a > $o] : (? [X4 : a] : (((X2 @ X4) != $true) & ((X0 @ X4) = $true)) & (((^[Y0 : a]: ((~ (X2 @ Y0)) & (X1 @ Y0))) = (^[Y0 : a]: ($false))) & ! [X3 : a] : (((X2 @ X3) = $true) | (((X1 @ X3) = $true) | ((X0 @ X3) != $true)))))),
% 1.00/0.90 inference(ennf_transformation,[status(thm)],[f7])).
% 1.00/0.90 thf(f7,plain,(
% 1.00/0.90 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((((^[Y0 : a]: ((~ (X2 @ Y0)) & (X1 @ Y0))) = (^[Y0 : a]: ($false))) & ! [X3 : a] : ((((X1 @ X3) != $true) & ((X0 @ X3) = $true)) => ((X2 @ X3) = $true))) => ! [X4 : a] : (((X0 @ X4) = $true) => ((X2 @ X4) = $true)))),
% 1.00/0.90 inference(flattening,[status(thm)],[f6])).
% 1.00/0.90 thf(f6,plain,(
% 1.00/0.90 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : ((((X0 @ X3) = $true) & ~((X1 @ X3) = $true)) => ((X2 @ X3) = $true)) & ((^[Y0 : a]: ((~ (X2 @ Y0)) & (X1 @ Y0))) = (^[Y0 : a]: ($false)))) => ! [X4 : a] : (((X0 @ X4) = $true) => ((X2 @ X4) = $true)))),
% 1.00/0.90 inference(rectify,[status(thm)],[f5])).
% 1.00/0.90 thf(f5,plain,(
% 1.00/0.90 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : ((((X0 @ X3) = $true) & ~((X1 @ X3) = $true)) => ((X2 @ X3) = $true)) & ((^[Y0 : a]: ((~ (X2 @ Y0)) & (X1 @ Y0))) = (^[Y0 : a]: ($false)))) => ! [X6 : a] : (((X0 @ X6) = $true) => ((X2 @ X6) = $true)))),
% 1.00/0.90 inference(fool_elimination,[status(thm)],[f4])).
% 1.00/0.90 thf(f4,plain,(
% 1.00/0.90 ~! [X0 : a > $o,X1 : a > $o,X2 : a > $o] : ((! [X3 : a] : (((X0 @ X3) & ~(X1 @ X3)) => (X2 @ X3)) & ((^[X4 : a] : ($false)) = (^[X5 : a] : ((X1 @ X5) & ~(X2 @ X5))))) => ! [X6 : a] : ((X0 @ X6) => (X2 @ X6)))),
% 1.00/0.90 inference(rectify,[status(thm)],[f2])).
% 1.00/0.90 thf(f2,negated_conjecture,(
% 1.00/0.90 ~! [X0 : a > $o,X2 : a > $o,X1 : a > $o] : ((! [X3 : a] : (((X0 @ X3) & ~(X2 @ X3)) => (X1 @ X3)) & ((^[X3 : a] : ($false)) = (^[X3 : a] : ((X2 @ X3) & ~(X1 @ X3))))) => ! [X3 : a] : ((X0 @ X3) => (X1 @ X3)))),
% 1.00/0.90 inference(negated_conjecture,[status(cth)],[f1])).
% 1.00/0.90 thf(f1,conjecture,(
% 1.00/0.90 ! [X0 : a > $o,X2 : a > $o,X1 : a > $o] : ((! [X3 : a] : (((X0 @ X3) & ~(X2 @ X3)) => (X1 @ X3)) & ((^[X3 : a] : ($false)) = (^[X3 : a] : ((X2 @ X3) & ~(X1 @ X3))))) => ! [X3 : a] : ((X0 @ X3) => (X1 @ X3)))),
% 1.00/0.90 file('/export/starexec/sandbox2/tmp/tmp.6MKDivwwtP/DTF2THF_1594.p',cTHM269_pme)).
% 1.00/0.90 thf(f28,plain,(
% 1.00/0.90 ((sK2 @ sK3) = $true)),
% 1.00/0.90 inference(trivial_inequality_removal,[status(thm)],[f25])).
% 1.00/0.90 thf(f25,plain,(
% 1.00/0.90 ($false = $true) | ((sK2 @ sK3) = $true)),
% 1.00/0.90 inference(superposition,[status(thm)],[f24,f20])).
% 1.00/0.90 thf(f20,plain,(
% 1.00/0.90 ($true = (sK1 @ sK3))),
% 1.00/0.90 inference(subsumption_resolution,[status(thm)],[f19,f15])).
% 1.00/0.90 thf(f15,plain,(
% 1.00/0.90 ($true = (sK0 @ sK3))),
% 1.00/0.90 inference(cnf_transformation,[status(thm)],[f13])).
% 1.00/0.90 thf(f19,plain,(
% 1.00/0.90 ($true = (sK1 @ sK3)) | ($true != (sK0 @ sK3))),
% 1.00/0.90 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.00/0.90 thf(f18,plain,(
% 1.00/0.90 ($true = (sK1 @ sK3)) | ($true != $true) | ($true != (sK0 @ sK3))),
% 1.00/0.90 inference(superposition,[status(thm)],[f16,f14])).
% 1.00/0.90 thf(f14,plain,(
% 1.00/0.90 ( ! [X4 : a] : (($true = (sK2 @ X4)) | ((sK1 @ X4) = $true) | ((sK0 @ X4) != $true)) )),
% 1.00/0.90 inference(cnf_transformation,[status(thm)],[f13])).
% 1.00/0.90 thf(f24,plain,(
% 1.00/0.90 ( ! [X1 : a] : (($false = (sK1 @ X1)) | ((sK2 @ X1) = $true)) )),
% 1.00/0.90 inference(not_proxy_clausification,[status(thm)],[f23])).
% 1.00/0.90 thf(f23,plain,(
% 1.00/0.90 ( ! [X1 : a] : (((~ (sK2 @ X1)) = $false) | ($false = (sK1 @ X1))) )),
% 1.00/0.90 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.00/0.90 thf(f22,plain,(
% 1.00/0.90 ( ! [X1 : a] : ((((~ (sK2 @ X1)) & (sK1 @ X1)) = $false)) )),
% 1.00/0.90 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.00/0.90 thf(f21,plain,(
% 1.00/0.90 ( ! [X1 : a] : ((((^[Y0 : a]: ($false)) @ X1) = ((^[Y0 : a]: ((~ (sK2 @ Y0)) & (sK1 @ Y0))) @ X1))) )),
% 1.00/0.90 inference(argument_congruence,[status(thm)],[f17])).
% 1.00/0.90 thf(f17,plain,(
% 1.00/0.90 ((^[Y0 : a]: ((~ (sK2 @ Y0)) & (sK1 @ Y0))) = (^[Y0 : a]: ($false)))),
% 1.00/0.90 inference(cnf_transformation,[status(thm)],[f13])).
% 1.00/0.90 % SZS output end Proof for DTF2THF_1594
% 1.00/0.90 % (1808)------------------------------
% 1.00/0.90 % (1808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.00/0.90 % (1808)Termination reason: Refutation
% 1.00/0.90
% 1.00/0.90 % (1808)Memory used [KB]: 5500
% 1.00/0.90 % (1808)Time elapsed: 0.003 s
% 1.00/0.90 % (1808)Instructions burned: 2 (million)
% 1.00/0.90 % (1808)------------------------------
% 1.00/0.90 % (1808)------------------------------
% 1.00/0.90 % (1807)Success in time 0.011 s
%------------------------------------------------------------------------------